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pottersheep

  • 3 years ago

Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

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  1. TAKEBACKMATH
    • 3 years ago
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    okay I will show you:

  2. pottersheep
    • 3 years ago
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    thank you so much!

  3. pottersheep
    • 3 years ago
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    :(

  4. TAKEBACKMATH
    • 3 years ago
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    thinking

  5. pottersheep
    • 3 years ago
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    oh ok sorry

  6. TAKEBACKMATH
    • 3 years ago
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    sorry, it too late for me I will hand this over to lonesome else?

  7. pottersheep
    • 3 years ago
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    ok

  8. pottersheep
    • 3 years ago
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    thanks anyways

  9. Callisto
    • 3 years ago
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    Here it goes~ Have you learnt remainder theorem yet?

  10. Callisto
    • 3 years ago
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    @pottersheep Are you there??

  11. pottersheep
    • 3 years ago
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    Yes sorry, we have!

  12. Callisto
    • 3 years ago
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    So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?

  13. pottersheep
    • 3 years ago
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    ok one sec

  14. pottersheep
    • 3 years ago
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    So i'd sub in 2 for x

  15. Callisto
    • 3 years ago
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    Yup!

  16. pottersheep
    • 3 years ago
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    3?

  17. pottersheep
    • 3 years ago
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    sorryryyryryryr

  18. pottersheep
    • 3 years ago
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    Sorry what do I do with the b though?

  19. pottersheep
    • 3 years ago
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    4b -24

  20. Callisto
    • 3 years ago
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    Right, so for p(2), you get p(2) = 4b - 24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by x-a)

  21. pottersheep
    • 3 years ago
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    Right, okay

  22. Callisto
    • 3 years ago
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    And what is the remainder when p(x) is divided by x+1 ?

  23. pottersheep
    • 3 years ago
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    b - 5

  24. Callisto
    • 3 years ago
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    Not really.. Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?

  25. pottersheep
    • 3 years ago
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    Opps, sorry! I subbed in 1!

  26. pottersheep
    • 3 years ago
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    9??

  27. pottersheep
    • 3 years ago
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    b + 9!

  28. Callisto
    • 3 years ago
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    Yes. Note that the remainder is p(x) = R when p(x) is divided by x-a. Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]

  29. pottersheep
    • 3 years ago
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    True, sorry!

  30. Callisto
    • 3 years ago
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    From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?

  31. Callisto
    • 3 years ago
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    Oh.. It's okay!

  32. pottersheep
    • 3 years ago
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    Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!

  33. Callisto
    • 3 years ago
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    Yes. Since they have the SAME remainder! You're welcome :)

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